The simple answer is that Britain did violate the Monroe Doctrine. Britain retained it's colonial holdings in the Caribbean for over a century in some cases. The Monroe Doctrine was promulgated at the end of 1823 (Sexton, The Monroe Doctrine), and Britain still had Jamaica, Barbados, the Leeward Islands, and the Ceded Islands. These were not backwaters, but instead still thriving commercial colonies with wealthy absentee planters getting rich off sugar and the labor of thousands of slaves (Ragatz, Fall of the Planter Class, among others). Slavery was ended in the colonies in 1838, while the United States maintained it's slave system for another 25 years. The British, having emancipated their slaves, sent abolitionists into their former North American colonies to organize and campaign for abolition, enraging planters and their northern allies (Walters Antislavery Appeal).

Further, the British held Canada and the dividing line at 49 degrees parallel was only extended to the west coast after extensive political fighting. The Oregon boundary dispute and the phrase "54'40" or Fight" are popular items in US History textbooks, though they rarely mention them in connection with the Monroe Doctrine.

Really the Monroe Doctrine was about American self assertion over political realism in Europe. The fledgling United States had hardly won the ability to prevent it's sailors from being pressed into the British Navy, let alone have the power to defend the hemisphere from Europe. The Doctrine becomes more important over the course of the 19th and 20th centuries as the revolutions in South America took place, and the countries began winning independence. Really, the best work to look at the significance and development of the Monroe Doctrine is Sexton, The Monroe Doctrine which carries it's investigation into the Spanish-American War, and is both recent and cheap.